A378242 - OEIS

%I #8 Nov 24 2024 09:31:01

%S 0,1,4,6,11,19,24,27,29,36,50,66,71,92,105,112,114,117,122,140,154,

%T 170,179,186,196,201,218,249,265,277,297,325,328,381,386,407,441,446,

%U 449,459,469,471,481,501,513,523,544,592,607,614,624,681,701,715,753,775

%N Lexicographically earliest sequence of nonnegative integers such that each term does not belong to a Fibonacci-like sequence starting with two earlier terms.

%C In other words, for any n > 0, a(n) is as small as possible so as not to belong to a sequence F defined by F(0) = a(i), F(1) = a(j) for some i, j < n, and then F(k+2) = F(k) + F(k+1).

%C By necessity, the sequence is strictly increasing.

%H Rémy Sigrist, <a href="/A378242/b378242.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A378242/a378242.txt">C++ program</a>

%e We can take a(1) = 0, as the first term is only required to be nonnegative.

%e We cannot take a(2) = 0, as 0 belongs to the Fibonacci-like sequence starting with 0 and 0.

%e We can take a(2) = 1.

%e From now on, we can no longer choose a Fibonacci number.

%e We can take a(3) = 4, the first nonnegative number that is not a Fibonacci number.

%o (C++) // See Links section.

%Y Cf. A378243, A378244.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Nov 20 2024